Ensure you check for all the screws holding the LU to the midsection. Some engines have 2 on each side at the AV plate point of separation. Some have an additional nut at the front of the casting and some had another screw hidden under the trim tab. To access that one you have to come in from the top to get the bolt holding the TT on then from underneath the AV plate to get the screw holding the LU to the midsection. If the LU doesn't even want to think about separating, look for a bolt/nut you missed.
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2 schools of thought on set up prior to removal. Some go for placing the shifter in N before you start the disassy and others prefer F gear which allows you to turn the drive shaft with the propeller when attempting to line up the male splines on the top of the drive shaft to fit into the female splined socket on the bottom of the crankshaft in the engine block.
I like N because N is easy to find...it's in the center of F and R. When time comes to insert the drive shaft, with the plugs out to relieve compression I just take the free hand and rotate the flywheel by hand. Oh, don't forget to lube the splines of the drive shaft prior to insertion with no grease on top....limits the travel up into the engine.
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On a 66 you may have a corrosion problem between the two mentioned above which will take some pulling and prying to get separated....don't pry on the alum casting....it's brittle and will break off if not careful.
The shift rod, from the shift lever up near the powerhead, fits over a short, splined, shifter shaft in the lower unit that can come out of the shifter cam in the lower unit if you pull too hard on it......easy to do with corrosion usually everywhere. You DO NOT want to pull this shaft out as you will have to disassemble the LU to get it back in the shifter cam.
When doing the separating, I like to lube things up real good with penetrating oil and hold the lower unit shift shaft with long nosed pliers while prying the upper shift shaft off the stub which I do as soon as I get enough space between the two to get some tools in there.....when you reassemble, ensure that the LU shift rod AND the upper shift lever are both in the N position so it will shift properly when operated.
I liked to put lubricant on the impeller blades to make insertion easier. My method of installation is (when ready for the cover installation), with the LU sitting on the skeg, vertical, on the floor, one hand is on the drive shaft.....vise grips work great....and the other hand is on the cover.....with the impeller blades sitting on top of the lower plate and the DRIVE KEY that fits in the notch in the impeller and the notch in the drive shaft ....so that when the DS turns the impeller turns too.....and then with a CLOCKWISE rotation of the drive shaft, put modest pressure on the cover and as you turn, the as the shaft is rotated and rotating the impeller, the blades will fold back and in one turn or maybe two, they will fold into the eccentric cavity of the cover and it can be seated on the lower plate......as best as I remember.
I don't know when Merc went from a carbon steel drive shaft to SS like OMC had forever it seems like. If yours had the carbon steel shaft, you obviously will have to clean all the rust and scale off before attempting to remove the WP cover.
HTH Good luck.